A battery backup sump pump is a device with a very limited scope of benefits - for a short power outage, the capacity of the sump itself will be adequate until power comes on again. For some particular scope of power outage and water flow a battery backup that's actually working well will keep you dry, and then for longer power outages or higher water flows the battery will expire before the power returns, and you get flooded anyway. Backup batteries eventually fail, and battery test routines are not always reliable, so you can never be quite sure exactly how long the battery will last in practice until you need it. Things to look for and/or ask about are the battery testing routine, the continuous run time or pumping volume from a battery charge at your required discharge lift (stats for 0 feet look great, but have no application to real life use) and whether an additional battery (preferably generic, such as golf-cart batteries) can be easily added, or if the pump is somehow dependent on a specialized and often expensive manufacturer-specific battery pack. At least check the cost of the replacement battery, and how often replacement is recommended, to get some idea of what you are getting into for ownership costs.
Are you on (city/town/some sort of public utility supplied) water? Does it provide water pressure when power is out? If so, a water-powered backup sump pump is going to be far more reliable than a battery-powered one. No batteries to fail, and few moving parts to fail, either.
If your water pressure vanishes with a power loss (ie, you have an electric well pump), that's not an option.
For possible failure of a normal electric-powered pump, having two pumps with different float settings can be sufficient, though it works better if you are the sort of person who will actually remember to change the float settings every year, so each one gets used as the "primary" pump. A smart pump controller that actually alternated pumps every time water needed to be pumped, and which ran both when one was not keeping up (or not working) would be nice, but I don't know if such a thing is actually made, other than having one custom-made. (Evidently they are made, though I have the impression that the market could stand a bit more competition to get the prices down to a more reasonable point.)
If there is any way to fix your drainage to not depend on a sump pump, that will cost you less in the long run even if it's fairly expensive to begin with. When that's not possible, it's arguable that a design error was made in the placement or depth of your house, and your mitigation options are on the one hand to make and maintain a considerable investment in battery backup sump pumps (and replacement batteries over time) or some type of auto-start generator and regular sump pumps, or to decorate and furnish (or simply use) the affected area in a manner that minimizes the impact of infrequent flooding when power outages and water ingress align (ceramic tile rather than carpet, etc.) You may also be able to increase your sump capacity (more, deeper, or larger sumps) to increase the amount of time between power loss and actual flooding at floor level.
Best Answer
By sizing the loads appropriately
Every load has a nameplate or published draw. You are to use the numbers on the various nameplates to assure that you are not overloading the circuit, or (more literally to Code), to assure you provide large enough circuit(s) for your loads.
You can get any ampacity of battery charger that you want.
You seem to be looking for an electronic solution; that's grossly over-complicated compared to simply sizing circuits (or appliances) correctly in the first place. But it is permitted in Code, mainly used for "load shedding" to allow an automatic transfer switch with a generator that is too small to pick up all provisioned loads. You couldn't use that gear here because it is monitoring for sagging voltage or AC frequency from the generator bogging, and that won't occur on a utility-supplied circuit wired with proper wiring. Unless the wiring is extremely long.
The DC pump is not powered by AC, it is powered by battery. The AC battery charger which refills the battery, does not need to be large enough to carry the full power of the pump, and it does not have a startup surge. So it might be 2-3 amps, leaving 12-13 amps for the AC pump.